<PRE><B>Question 248852</B>
******EDITED TO ADD THE FOLLOWING:******&lt;br&gt;

******As tutor Alan3354 pointed out, 2 is a prime number, so the following deductive reasoning works for all prime numbers except 2.  It was not a complete proof, just an idea of the difference between inductive and deductive reasoning.  I will edit the statement/answer below.******&lt;br&gt;  

To quickly follow up on this,&lt;br&gt;

We can use deductive reasoning in the following manner (this is NOT a complete proof, just an example of deductive reasoning).&lt;br&gt;  

As the other tutor stanbon said in the original answer, inductive reasoning is based on examples, deductive reasoning is based on the general case!&lt;br&gt;

Let x be any prime number EXCEPT 2 (which by definition will be odd, since it can not have 2 as a divisor).&lt;br&gt;

Let y be any prime number EXCEPT 2 (which can equal x, which will also be odd by definition).&lt;br&gt;

Since the sum of 2 odd numbers will always be even (using properties of integers), the sum of 2 prime numbers will also then be even.&lt;br&gt;

x + y = an even number&lt;br&gt;

The sum of any 2 prime numbers will always be even, unless ONLY ONE of those prime numbers is 2.  Of course if both of those prime numbers are 2, then you again have a sum that is an even number.  :)&lt;br&gt;</PRE>